PhysicsCBSE Class 12 · Sample paper, session 2023-24 · 3 marks · Short answer

CBSE Class 12 Physics sample paper 2023-24: question 22

From the official CBSE sample question paper for 2023-24, section C, question 22, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q22 · 3 marks · Short answerNuclei

A given coin has a mass of 3.0 g. Calculate the nuclear energy that would be required to separate all the neutrons and protons from each other. For simplicity assume that the coin is entirely made of $_{29}^{63} C u$ atoms (of mass 62.92960 u).
Given $m_{p}$ = 1.007825u and $m_{n}$ = 1.008665u.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

Open one hint at a time and try again before the next.

Hint 1

First find how many atoms are in 3 g using Avogadro's number and molar mass 63 g.

Hint 2

Mass defect = (mass of separate protons and neutrons) − nuclear mass; 1 u = 931.5 MeV.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Number of Cu atoms in 3.0 g: $N = \frac{6.023 \times 1 0 ^{23} \times 3}{63} = 2.87 \times 1 0^{22}$
½ mark
Each $_{29}^{63}$ Cu nucleus has 29 protons and $63 - 29 = 34$ neutrons.
Mass defect: $Δ m = 29 (1.007825) + 34 (1.008665) - 62.92960$
$= 29.226925 + 34.294610 - 62.92960 = 0.591935 u$
1 mark
Binding energy per nucleus: $E_{1} = 0.591935 \times 931.5 MeV = 551.4 MeV$
½ mark
Energy required for the whole coin: $E = N E_{1} = 2.87 \times 1 0^{22} \times 551.4 MeV \approx 1.58 \times 1 0^{25} MeV$ $(\approx 2.5 \times 1 0^{12} J)$
1 mark

Answer: ≈ 1.58 × 10^25 MeV (≈ 2.5 × 10^12 J)

Where the marks are

Number of atoms in 3 g ≈ $2.87 \times 1 0^{22}$ (½ mark)
Mass defect per atom ≈ 0.5919 u using 29 protons and 34 neutrons (1 mark)
Energy per atom = Δm × 931.5 MeV (½ mark)
Total energy ≈ $1.58 \times 1 0^{25}$ MeV (1 mark)

Revise the chapter

Chapter: Nuclei (notes, formulas, where marks are lost and every past question)
Topic: Mass Defect and Binding Energy

Practise this chapterBoard-style questions from Nuclei, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2023-24: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 12 Physics sample paper 2023-24: question 22

Hints

Step-by-step solution

Revise the chapter

More questions from Nuclei